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Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains

Sibel Şahin (2015)

Banach Center Publications

Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space H u p ( Ω ) is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces H u p ( Ω ) where the Monge-Ampère measure ( d d c u ) has compact support for the associated exhaustion...

Morera type problems in Clifford analysis.

Emilio Marmolejo Olea (2001)

Revista Matemática Iberoamericana

The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems.In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Specifically, we show the...

Morphisms of Klein surfaces.

F. J. Cirre (1997)

Revista Matemática de la Universidad Complutense de Madrid

We give an elementary proof of a theorem of Andreian Cazacu on the behavior of morphisms of Klein surfaces under composition.

Multiple prime covers of the riemann sphere

Aaron Wootton (2005)

Open Mathematics

A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

Multiplicative isometries on the Smirnov class

Osamu Hatori, Yasuo Iida (2011)

Open Mathematics

We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself, if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = f ϕ ¯ ¯ for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z 1, ..., z n) = ( λ 1 z i 1 , . . . , λ n z i n ) for |λ j| = 1, 1 ≤ j ≤ n, and (i 1; ..., i n)is some permutation of the integers from...

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